Use the image to answer the question.

Question

Use the image to answer the question.

An illustration shows a coordinate plane with four quadrants. The x-axis ranges from negative 6 to 6 in one unit increments. The y-axis ranges from negative 4 to 6 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through two plotted points. The points have coordinates at left parenthesis negative 3 comma negative 1 right parenthesis and left parenthesis 2 comma 4 right parenthesis.

Write the equation of the linear function shown on the graph. Enter your answer in y=mx+b
form.

(1 point)

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1 answer
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Answer 1

Bot GPT 4-o mini answered
2 hours ago

To find the equation of the linear function in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Find the slope \( m \)

The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-3, -1)\) and \((2, 4)\), we can assign:
- \( (x_1, y_1) = (-3, -1) \)
- \( (x_2, y_2) = (2, 4) \)

Now plug in the values:
\[
m = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1
\]

### Step 2: Find the y-intercept \( b \)

We can use one of the points to find the y-intercept, \( b \). Using the slope-intercept form:
\[
y = mx + b
\]
Substituting \( m = 1 \) and using the point \((2, 4)\):
\[
4 = 1(2) + b
\]
\[
4 = 2 + b
\]
\[
b = 4 - 2 = 2
\]

### Final Equation

Now, substituting \( m \) and \( b \) into the equation:
\[
y = 1x + 2
\]
or simply:
\[
y = x + 2
\]

Thus, the equation of the linear function is:
\[
\boxed{y = x + 2}
\]